2x^2+11x-16=0

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Solution for 2x^2+11x-16=0 equation:


Simplifying
2x2 + 11x + -16 = 0

Reorder the terms:
-16 + 11x + 2x2 = 0

Solving
-16 + 11x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-8 + 5.5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 5.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 5.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5.5x + x2 = 0 + 8
5.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
5.5x + x2 = 8

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 8 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 8 + 7.5625

Combine like terms: 8 + 7.5625 = 15.5625
7.5625 + 5.5x + x2 = 15.5625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x + 2.75) equal to 3.94493346 and -3.94493346.

Subproblem 1

x + 2.75 = 3.94493346 Simplifying x + 2.75 = 3.94493346 Reorder the terms: 2.75 + x = 3.94493346 Solving 2.75 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.94493346 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.94493346 + -2.75 x = 3.94493346 + -2.75 Combine like terms: 3.94493346 + -2.75 = 1.19493346 x = 1.19493346 Simplifying x = 1.19493346

Subproblem 2

x + 2.75 = -3.94493346 Simplifying x + 2.75 = -3.94493346 Reorder the terms: 2.75 + x = -3.94493346 Solving 2.75 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.94493346 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.94493346 + -2.75 x = -3.94493346 + -2.75 Combine like terms: -3.94493346 + -2.75 = -6.69493346 x = -6.69493346 Simplifying x = -6.69493346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.19493346, -6.69493346}

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